Bone elongation in children occurs through the process of endochondral ossification in cartilaginous growth plates at the ends of long bones. Clonal expansion of stem cells results in columns of chondrocytes whose spatial position within the growth plate mirrors their differentiation stage: cellular proliferation, cellular enlargement (hypertrophy), and cellular apoptotic death followed by replacement of bone on the previously calcified cartilaginous matrix (FIG. 1). The extent of the bone elongation achieved depends on the kinetics of chondrocytic activity at each stage of differentiation, and on the rate of regulated transitions between stages. A complex interplay of genetic and epigenetic factors (e.g. endocrine, paracrine, autocrine, nutritional, biomechanical) influences postnatal longitudinal bone growth by acting primarily at the cellular level through differential effects at specific phases of chondrocytic development and maturation.
The growth plate chondrocytes are anisotropically distributed in the columns that parallel the bone elongation direction, and the columns spatially represent the temporal differentiation cascade of each individual chondrocyte. During this differentiation cascade, chondrocytes complete multiple cellular cycles. Their post-proliferative terminal differentiation is characterized by a significant volume increase during hypertrophy. A critical concept in understanding how longitudinal growth is achieved during the differentiation cascade is that, as cells hypertrophy, they undergo a regulated shape change, and the orientation of the long axis of the cell changes relative to the long axis of the bone.
For example, proliferative cells that had an average height of approximately 10 μm in the direction of growth, become hypertrophic cells with an average height of 25-30 μm in the direction of growth. The sum of each cell's incremental height change multiplied by the number of cells turned over in a day is the single most significant variable accounting for the amount of growth achieved by a given growth plate (Breur et al., 1991; Farnum, 1994; Farnum and Wilsman, 2001 and 2002).
Multiple stereological-based approaches have been used to understand and model this important shape change of growth plate chondrocytes during the differentiation cascade. Chondrocytes can exhibit an elongated shape in certain sections of the tissue. (Buckwalter et al., 1985; Farnum, 1994). Buckwalter et al. (1985) applied methods based on equations involving the intersections of cells with a grid of parallel lines. They quantified the orientation distribution of each cell relative to the other cells in the group and appraised chondrocytic shape in reference to the chondrocytic phase in the growth plate. However, these methods and studies have not provided explanations or mechanisms for anisotropic growth of connective tissue, and in particular have not provided mechanisms that allow for the prediction and possible alteration of growth.
It is therefore desirable for identification of such mechanisms for connective tissue growth, along with methods and apparatus for testing, measuring, and altering such mechanisms.